Proton-proton interactions resulting in final states with two photons are studied in a search for the signature of flavor-changing neutral current interactions of top quarks ($t$) and Higgs bosons ($H$). The analysis is based on data collected at a center-of-mass energy of 13 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of $137\text{ }\text{ }{\mathrm{fb}}^{-1}$. No significant excess above the background prediction is observed. Upper limits on the branching fractions ($\mathcal{B}$) of the top quark decaying to a Higgs boson and an up ($u$) or charm ($c$) quark are derived through a binned fit to the diphoton invariant mass spectrum. The observed (expected) 95% confidence level upper limits are found to be 0.019% (0.031%) for $\mathcal{B}(t→Hu)$ and 0.073% (0.051%) for $\mathcal{B}(t→Hc)$. These are the strictest upper limits yet determined.

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